,Uses,"Fact about"
"Hall and hyperfocal implies retract",,"Hall subgroup; 3,Hyperfocal subgroup; 1,Retract; 3,Hall retract; 1,Normal complement; 3"
"Hall implies join of Sylow subgroups","Sylow subgroups exist,Sylow of Hall implies Sylow,Lagrange's theorem","Hall subgroup; 2,Join of Sylow subgroups; 2"
"Hall implies paracharacteristic","Hall implies join of Sylow subgroups,Sylow implies paracharacteristic,Paracharacteristicity is strongly join-closed","Hall subgroup; 2,Paracharacteristic subgroup; 2"
"Hall is transitive","Index is multiplicative,Lagrange's theorem","Hall subgroup; 1,Transitive subgroup property; 2"
"Hall satisfies intermediate subgroup condition","Index is multiplicative","Hall subgroup; 1,Intermediate subgroup condition; 2"